Question

resolva a equação:
(2/x²-1 ) -2 = X/x-1
Obs: Com x € IR, x diferente de -1 e x diferente de +1

Answer 1

            2                           x                                           x (x² - 1)
------------------- - 2 = -----------------   ⇒   2 - 2(x² - 1) = --------------------      ⇒
         x² - 1                     x - 1                                              x - 1


                             x (x + 1)(x - 1)
⇒   2 - 2x² + 2 = ----------------------------   ⇒  -2x² + 4 = x (x + 1)    ⇒    
                                    x - 1

-2x² + 4 = x² + x    ⇒       -2x²  - x² + 4 - x = 0   ⇒   -3x² -x + 4 = 0

                                                    -b +_ √Δ
Pela fórmula de Báskhara x = ----------------- , Δ = b² -4ac, a= -3, b= -1 ,  
                                                        2. a
c=4

Substituindo em Δ, vem Δ = (-1)² - 4(-3)(4) = 1 + 48 = 49

                                                                     - (-1) +_ √49      1 +_  7
substituindo na fórmula de Báskhara   x = ------------------- = ------------  ∴
                                                                           2(-3)                 -6 

          1 - 7           -6                           1 + 7          8                4
x' = ------------  = ------  = 1    e   x'' = ---------- = ---------  = -  -------
             -6            -6                              -6            -6                3

Porém, x ≠ -1 e x ≠ 1, logo x' não serve. Portanto, a resposta é x= - 4/3

Resp.: x = - 4/3